GIven
the height of the cylinder is 150ft
diameter of hemisphere and the cylinder is 20ft
radius = d/2
then the height of hemisphere is equal to the radius of it
height of the hemisphere = 10
[tex]\begin{gathered} \text{radius}=\frac{20}{2} \\ r=10 \end{gathered}[/tex]
volume of the silo = volume of the cylinder + volume of the hemisphere
first we find the volume of the cylinder
[tex]\begin{gathered} \text{volume of the cylinder = }\pi r^2h \\ =\pi(10)^2(150) \\ =\pi100(150) \\ =15000\pi \end{gathered}[/tex]
now we find the volume of the hemisphere
[tex]\begin{gathered} \text{volume of hemisphere =}\frac{2}{3}\pi r^3 \\ =\frac{2}{3}\pi(10)^3 \\ =\frac{2}{3}\pi(1000) \end{gathered}[/tex]
now we calculte the volume of the silo
[tex]\begin{gathered} \text{volume of silo=}15000\pi+\frac{2}{3}\pi(1000) \\ =\pi(15000+\frac{2}{3}(1000)) \\ =\pi(15000+\frac{2000}{3})_{} \\ =\pi(15000+666.6) \\ =\pi(15666.6) \\ =\frac{22}{7}(15666.6) \\ =49237.8cubicft \end{gathered}[/tex]
